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Title: derivatives formulas
Description: formualas
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Symbolab Derivatives Cheat Sheet
Derivative Rules:
 Power Rule:



𝑑

(𝑥 𝑎 ) = 𝑎 ⋅ 𝑥 𝑎−1
𝑑𝑥

Derivative of a Constant:

𝑑

𝑑𝑥

Sum/Difference Rule:
(𝑓 ± 𝑔)′ = 𝑓 ′ ± 𝑔′

Common Derivatives:
𝑑
1
(ln(𝑥)) =




𝑑𝑥
𝑑
𝑑𝑥
𝑑
𝑑𝑥

𝑥

(ln(|𝑥|)) =
(𝑒

𝑥)

= 𝑒



𝑑

𝑑𝑥
𝑑
𝑑𝑥

1



𝑑

𝑑𝑥
𝑑
𝑑𝑥




𝑑𝑥
𝑑
𝑑𝑥



𝑑

𝑑𝑥
𝑑
𝑑𝑥

𝑓 ′



Chain Rule:



(cos(𝑥)) = − sin(𝑥)



(tan(𝑥)) = sec 2 (𝑥)



1

(arccos(𝑥)) = −
(arctan(𝑥)) =

√1−𝑥 2
1

𝑥 2 +1







(cosh(𝑥)) = sinh(𝑥)



(tanh(𝑥)) = sech2 (𝑥)



Arc Hyperbolic Derivatives:
𝑑
1
 𝑑𝑥 (arcsinh(𝑥)) = √𝑥 2


Quotient Rule: ( 𝑔) =



𝑥

Hyperbolic Derivatives:
𝑑
(sinh(𝑥)) = cosh(𝑥)

𝑑𝑥
𝑑



𝑥

Arc Trigonometric Derivatives:
𝑑
1
 𝑑𝑥 (arcsin(𝑥)) = √1−𝑥 2


Constant Out: (𝑎 ⋅ 𝑓)′ = 𝑎 ⋅ 𝑓 ′



Trigonometric Derivatives:
𝑑
 𝑑𝑥 (sin(𝑥)) = cos(𝑥)


(𝑎) = 0



(arccosh(𝑥)) =
(arcsech(𝑥)) =

+1
1

√𝑥−1√𝑥+1
√

2
−1
𝑥+1

𝑥⋅(𝑥−1)





𝑑
𝑑𝑥
𝑑
𝑑𝑥

𝑑
𝑑𝑥
𝑑
𝑑𝑥
𝑑
𝑑𝑥

𝑑
𝑑𝑥
𝑑
𝑑𝑥
𝑑
𝑑𝑥

𝑑
𝑑𝑥
𝑑
𝑑𝑥
𝑑
𝑑𝑥

𝑑
𝑑𝑥
𝑑
𝑑𝑥
𝑑
𝑑𝑥

𝑑𝑓(𝑢)
𝑑𝑥

(log(𝑥)) =

(csc(𝑥)) =
(cot(𝑥)) =

𝑑𝑓

=

𝑔2
𝑑𝑢

⋅

𝑑𝑢

𝑑𝑥

1
𝑥⋅ln(10)
1

(log 𝑎 (𝑥)) =

(sec(𝑥)) =

𝑓 ′ ⋅𝑔−𝑔′ ⋅𝑓

𝑥⋅ln(𝑎)

tan(𝑥)
cos(𝑥)
− cot(𝑥)
sin(𝑥)
1
− sin2(𝑥)

(arcsec(𝑥)) =

1
√𝑥 2 (𝑥 2 −1)

(arccsc(𝑥)) = −
(arccot(𝑥)) = −

1

|𝑥|√𝑥 2 −1
1
𝑥 2 +1

(sech(𝑥)) = − sech(𝑥) ⋅ tanh(𝑥)
(csch(𝑥)) = − coth(𝑥) ⋅ csch(𝑥)
(coth(𝑥)) = − csch2 (𝑥)

(arctanh(𝑥)) =

1
1−𝑥 2

(arccsch(𝑥)) = −
(arccoth(𝑥)) =

1

1
1

𝑥 2 √ 2 +1
𝑥

1−𝑥 2

Title: derivatives formulas
Description: formualas
Buy These NotesPreview